Uncertainty in poker stems from two key sources, the shuffled deck and an adversary whose strategy is unknown. One approach is to find a pessimistic game theoretic solution (i.e. a Nash equilibrium), but human players have idiosyncratic weaknesses that can be exploited if a model of their strategy can be learned by observing their play. However, games against humans last for at most a few hundred hands so learning must be fast to be effective. We explore two approaches to opponent modelling in the context of Kuhn poker, a small game for which game theoretic solutions are known. Parameter estimation and expert algorithms are both studied. Experiments demonstrate that, even in this small game, convergence to maximally exploitive solutions in a small number of hands is impractical, but that good (i.e. better than Nash or breakeven) performance can be achieved in a short period of time. Finally, we show that amongst a set of strategies with equal game theoretic value, in particular the set of Nash equilibrium strategies, some are preferable because they speed learning of the opponent’s strategy by exploring it more effectively.

Content Area: 12. Machine Learning

Subjects: 1.8 Game Playing; 12. Machine Learning and Discovery

Submitted: May 10, 2005

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